A356971 E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x^3 * A(x)).

1, 0, 0, 0, 24, 60, 240, 1260, 108864, 1149120, 12160800, 138045600, 5605649280, 122049607680, 2378318604480, 45712559692800, 1529842399303680, 47673689320857600, 1382823169839820800, 38831806109898547200, 1378613101427645184000

Offset: 0

Author

Seiichi Manyama, Sep 07 2022

Keywords

• nonn

Crossrefs

Cf. A184949, A349556, A356970.

Cf. A356968.

Programs

Mathematica

m = 21; (* number of terms *)
A[_] = 0;
Do[A[x_] = 1/(1 - x*A[x])^(x^3*A[x]) + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Sep 12 2022 *)

PARI

a(n) = n!*sum(k=0, n\4, (n-2*k+1)^(k-1)*abs(stirling(n-3*k, k, 1))/(n-3*k)!);

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (n-2*k+1)^(k-1) * |Stirling1(n-3*k,k)|/(n-3*k)!.